Different mean functions for the Gaussian process

[HeltonSM]

Is it possible to define the mean function for the Gaussian process.

A quadratic one for example?

If so, can you provide the syntax for that?

Thank you.

[uremes]

Hi! This is an old question but I decided to comment in case someone else would also need this.

ELFI uses GPy models which take a mean function as input parameter. The available mean functions are listed here, but it is also possible to create a custom one. For example @jankokk used this in his thesis:

import numpy as np
import GPy

class Polynomial(GPy.core.Mapping):

    def __init__(self, input_dim, output_dim, name='polymap'):

        super(Polynomial, self).__init__(input_dim=input_dim, output_dim=output_dim, name=name)

        self.A = GPy.core.Param('A', np.random.rand(self.input_dim, self.output_dim))
        self.B = GPy.core.Param('B', np.random.rand(self.input_dim, self.output_dim))
        self.C = GPy.core.Param('C', np.random.rand())

        self.link_parameter(self.A)
        self.link_parameter(self.B)
        self.link_parameter(self.C)

        self.A.constrain_positive()

    def f(self, X):

        XX = np.power(X, 2)
        return np.dot(XX, self.A) + np.dot(X, self.B) + self.C

    def update_gradients(self, dL_dF, X):

        XX = np.power(X, 2)
        self.A.gradient = np.dot(XX.T, dL_dF)
        self.B.gradient = np.dot(X.T, dL_dF)
        self.C.gradient = np.sum(dL_dF, axis=0)

And how to use a mean function in BOLFI:

import elfi
from elfi.examples import ma2

seed = 230112

m = ma2.get_model(seed_obs=seed)
bounds = {'t1':(-2, 2), 't2':(-1, 1)}

# Gaussian process model
mean_function = Polynomial(2, 1)
target_model = elfi.GPyRegression(m.parameter_names, bounds=bounds, mean_function=mean_function)

# BOLFI
bolfi = elfi.BOLFI(m['d'], initial_evidence=20, update_interval=10, target_model=target_model, seed=seed)